It is known that CD is the height of AB side in △ ABC, AC + BC = 8, CD = 2, AE is the diameter of circumscribed circle of △ ABC, (1) try to explain △ CBD ∽ AEC, (2) let AC = x, AE = y, find the functional relation of y with respect to x, and (3) find the maximum value of Y

It is known that CD is the height of AB side in △ ABC, AC + BC = 8, CD = 2, AE is the diameter of circumscribed circle of △ ABC, (1) try to explain △ CBD ∽ AEC, (2) let AC = x, AE = y, find the functional relation of y with respect to x, and (3) find the maximum value of Y

(1) It is proved that: connecting BC, ∵ CD is the height of AB side in △ ABC, ∵ CDB = 90 °, ∵ AE is the diameter of circumscribed circle of △ ABC, ∵ ace = 90 °, ∵ ace = ∵ CDB, ∵ e = ∵ B, ∵ CBD ∽ AEC; (2) ∵ CBD ∽ AEC, ∵ CDAC = bcae, ∵ AC = x, AE = y, AC + BC = 8, CD = 2, ∵ BC = 8-x, ∵ 2x = 8 − XY, ∵ y. The functional relationship of X with respect to X is y = - 12x2 + 4x; (3) ）∵ y = − 12x2 + 4x = - 12 (x-4) 2 + 8, and the maximum value of Y is 8

As shown in the figure, in the triangle ABC, ∠ B = 45 ° and CD and AE are its two heights

Let be be x, then according to the cosine theorem: de ^ 2 = be ^ 2 + BD ^ 2-2be * BD * cos45. (1) AC ^ 2 = AB ^ 2 + BC ^ 2-2ab * BC * cos45. (2) because AB * CD = BC * AE (equal area), and AE = be, BD = CD (isosceles right triangle), so: BD = radical 2 / 2, BC is substituted into (1) to get de ^ 2 = 1 / 2 * AC ^ 2

In the triangle ABC, ab = 15, BC = 14, CA = 13, find the height ad on the side of BC
Write clearly step by step, don't write "/" or "*", don't understand

Let CD be X. according to the Pythagorean law, in a triangle ADC, let x denote ad, and BD = 14-x. the solution of Pythagorean law is x = 5, so the height is 12

As shown in the figure, in △ ABC, it is known that ab = BC = CA = 4cm, ad ⊥ BC is at D, and points P and Q start from B and C at the same time, where point P moves along BC to terminal C with a speed of 1cm / s, and Q moves along Ca and AB to terminal B with a speed of 2cm / s. let their motion time be x (s). ① when calculating the value of X, PQ ⊥ AC? ② When 0 ＜ x ＜ 2, can ad divide the area of △ PQD equally? If yes, please explain the reason; ③ to explore the position relationship between PQ diameter circle and AC, please write the value range of X of the corresponding position relationship (writing process is not required)

(1) When q is on AB, it is obvious that PQ is not perpendicular to ac. when q is on AC, BP = x, CQ = 2x, PC = 4-x; ∵ AB = BC = CA = 4, ∵ C = 60 °; if PQ ⊥ AC, then ∵ QPC = 30 °, PC = 2cq, ∵ 4-x = 2 × 2x, ∵ x = 45; (2) when 0 ＜ x ＜ 2, in RT △ QPC, QC

In isosceles △ ABC, ab = AC, ∠ BAC = 36 & ordm;, AE is the bisector of △ ABC, BF is the bisector of ∠ ABC, and BF is the intersection of the extension of BF
AE at point E (1) shows that AF = FB = BC (2) EF / BF = BC / FC

(1) Because AB = AC, so angle ABC = angle c, because angle a = 36 degrees, so angle ABC = angle c = 72 degrees, because BF bisects angle ABC, so angle ABF = angle ABC / 2 = 36 degrees, angle BFC = angle a + angle ABF = 36 + 36 = 72 degrees, so angle FBC = angle c, angle a = angle ABF = 36 degrees, so BF = BC, AF = BF, so AF = FB = BC (2) because AE is the outer angle

As shown in the figure, in the triangle ABC, the triangle ABC = 90 degrees, ad is perpendicular to point D, and E is the point on ad? Prove angle c = angle bad prove angle bed > angle C
As shown in the figure, in the triangle ABC, the triangle ABC is 90 degrees, ad is perpendicular to point D, and E is the point on ad. prove that angle c = angle bad; prove that angle bed > angle C. please reply as soon as possible

According to the question, angle BAC should be 90 degrees, angle c + angle B = 90 degrees, angle bad + angle bad = 90 degrees, so angle c = angle bad

As shown in the figure, ad is the height of △ ABC, be bisects ∠ ABC and intersects ad with E. if ∠ C = 70 ° and ∠ bed = 64 °, calculate the degree of ∠ BAC

∵ ad is the height of △ ABC, ∵ C = 70 °, ∵ DAC = 20 °, ∵ be bisection ∵ ABC intersects ad with E, ∵ Abe = ∵ EBD, ∵ bed = 64 °, ∵ Abe + ∵ BAE = 64 °,